Drugs can be percutaneously delivered to patients to treat many different medical conditions. In many cases, these drugs are delivered into subdermal tissue. For example, the drugs can be injected via a needle that is inserted into the subdermal tissue of the patient or can be pumped through a catheter that is positioned within the subdermal tissue of the patient. Some drugs can be delivered intradermally (i.e., within the dermis of the patient). Intradermal drug delivery can be carried out, for example, by injecting the drug via a very small needle (i.e., a microneedle) inserted into the dermis of the patient.